But the US president is also chief policy-maker, head of the executive branch, the actual commander-in-chief, manager of the economy and leader of their party.
New Zealand would almost certainly split these two types of roles. At most, our president would be like those of Singapore and Ireland, or India and Germany.
All four are largely ceremonial, like King Charles and Dame Cindy. In Singapore and Ireland they are elected directly by the public and tend to be well-regarded former politicians.
In India and Germany, voters aren't involved. Instead, their federal and state parliaments form electoral colleges to choose.
Based on a partnership interpretation of Te Tiriti and the Treaty of Waitangi, some Māori might advocate an electoral college with iwi holding half the seats. It wouldn't really matter much if the president's powers were limited to those of a governor-general. No doubt the country's name would be debated.
Most likely, pragmatic New Zealanders would keep the current convention for appointing a governor-general. In practice, the prime minister decides with the acquiescence of the Opposition. At least since 1980, it has worked perfectly well.
Choosing a selection process can't be divorced from the powers the president would have.
If limited to those of King Charles, Dame Cindy, Ireland's Michael Higgins or Germany's Frank-Walter Steinmeier, Ardern would be exceptional.
Ardern may have failed utterly as chief policy-maker, head of the executive branch and manager of the economy, but New Zealand has had no better symbolic leader of the nation and top official diplomat.
Ardern could easily add head of state and ceremonial commander-in-chief to those roles. That would leave a future Prime Minister Michael Wood or Nicola Willis to concentrate on operating the levers of government to deliver their party's objectives, a role for which Ardern has sadly proven so unsuited.
There are other options. A head of state need not be an individual. Switzerland's is a seven-person committee. If that sounds radical, New Zealand's existing arrangements are more so.
The Constitution Act 1986 says our head of state is the sovereign in right of New Zealand, but doesn't say explicitly who that is. It's certain the King of New Zealand is not the same thing as the King of the United Kingdom, even though one person holds both jobs.
Foreign governments already treat Dame Cindy as head of state when she visits. Likewise, she acts that way when they call.
Then there's "the Crown". No one is sure what it is. Some say it is the jewelled headgear we saw on Queen Elizabeth's coffin or whoever wears it. But it can't be either since everyone agrees the Crown of New Zealand is different from the Crown of the UK.
Some think it's just an abstract term for the set of powers that UK monarchs once had.
But no one in New Zealand ever had those powers. And the Crown of New Zealand can't be King Charles because it's agreed he only personifies it.
In practise, the position of head of state of New Zealand is already empty and the system works perfectly well on that basis. A governor-general must do whatever their prime minister advises as long as that prime minister has a majority in Parliament.
If that's not clear, then theoretically a governor-general might have to choose who should be prime minister. Whenever that looks possible, governors-general have done the right thing — by doing nothing.
An exception may be 1984 when Sir Robert Muldoon refused to take instructions from the incoming Government in the days between the election and the handover of power, causing a currency crisis.
It was rumoured Governor-General Sir David Beattie would sack Muldoon if advised accordingly by Deputy Prime Minister Jim McLay and the rest of Cabinet. The rumour was enough to force Muldoon into line.
In 1993, with no clear election-night result, Governor-General Dame Catherine Tizard asked Sir David to set up a committee of three retired appeal court judges to advise her on who to pick as prime minister if necessary. Special voters meant it wasn't.
Before the first MMP election in 1996, Governor-General Sir Michael Hardie Boys made clear politicians must work everything out, not him.
That rule remains. Governors-General have been as patient as everyone else during Winston Peters' coalition talks. When Prime Minister Jenny Shipley sacked Peters and ended the National-NZ First coalition, Sir Michael — as promised — did nothing, waiting to see if Shipley could get 61 MPs. She did.
With some polls indicating a 60-60 dead heat between Labour-Green-Te Pāti Māori and National-Act, Dame Cindy could potentially have decisions to make — but probably not.
In a dead heat, Ardern and Christopher Luxon would try to attract a disgruntled MP across the divide. Ardern might reach out to, say, National's Harete Hipango, who famously "paddles her own waka". Luxon might bet former police union boss Greg O'Connor could back a weak National Government over anti-prison Greens.
If that all failed, Ardern and Luxon could agree on a temporary caretaker Government for the rest of 2023. If not, the only solution would be another election. But that would all be obvious, either to Dame Cindy or to a president with her powers.
If a governor-general or president appointed a prime minister who wasn't backed by 61 MPs, Parliament would vote them out the next day and the process would start again.
That makes it unthinkable any governor-general or president ever would.
With Parliament not just democratically but proportionally elected, the median voter is already sovereign, not King Charles.
If a head of state would never in practise make a decision, we are not limited to an individual or even a Swiss-style committee.
What were known as the Whanganui River and Te Urewera National Park were confirmed to be persons by the previous National Government. If you baulk at Ardern, John Key or Helen Clark as head of state, why not give, say, Aoraki Mount Cook the role? We could decide, including for Treaty of Waitangi interpretation, that it would personify what was previously known as the Crown, the way King Charles merely personifies the Crown today.
Like him, it would be represented by someone like Dame Cindy in a role with the same powers as the current Governor-General and appointed in the same way.
This would make no difference to how our political system operates. We would be a republic, if that is so important to some people, without changing anything, and without the divisive process of deciding which of the so-called team of five million should be top dog.
- Matthew Hooton is an Auckland-based public relations consultant.